If I Had A Rope Around The Circumference Of The Earth, And I Wanted Then To Extend This Rope So That It Was Always One Meter Away From The Earth, How Much More Rope Would I Need?

When doing a question like this ALWAYS draw a diagram.  For this, draw a circle, lable the information you know, and establish what you need to find!

well the circumference of the earth is 40008 km

Do you know the equation to find the circumference?

Use this equation to calculate the radius of the earth.

Now you want the new length of rope to always be one meter away from the earth, so this would actually increase the Diameter by 2 meters.  So add to meters to your original radius answer, then using the same circumference equation, substitute your new radius/Diameter value.

******

Lets get going

C = (Pi)(D)
40008 = 3.14(D)
40008/3.14 = D
12741.4 = D

So the earth Diameter is D - but you want your rope to be one meter away from the earths surface, so this will mean the diameter you need to use is 12741.4 + 2 (one meter on each side)

Now recalculate the Circumference

C = (Pi)(D)   [12743.4]

C = (3.14)(12743.4)

C = 40014.28

thanked the writer.
The circumference is
(original circumference) = 2*Pi*R,
where Pi ≈ 3.14159, and R = radius of the Earth.

Add 1 meter to R and you get
(new circumference) = 2*Pi*(R + 1 m) = 2*Pi*R + 2*Pi*(1 m)

Then
(new circumference) - (original circumference) = 2*Pi*R + 2*Pi*(1 m) - 2*Pi*R
= 2*Pi*(1 m) ≈ 6.28318 m
thanked the writer.